Question

Please help, will give medal!

Answer 1

What is the taxidistance between (8, 17) and (21, 32)?


If AR = 12 m and RE = 3 m, what is the ratio of the areas of triangle ARH and triangle AES?

Answer 2

There should be a figure.

Answer 3

For the second one? Yeah just a second.

Answer 4

For the first one -

Use distance formula :

If you have 2 points : \(A(x_1,y_1) \space \& \space B (x_2,y_2)\)

Then the distance between these two points is :

\(AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 } \)

Answer 5

so apparently the first one should be about 17

Answer 6

However, my options are
44
36
28
20

Answer 7

For the second one -

Use this theorem :

\(\text{In two similar triangles, the ratio of their areas is the square of the ratio of their sides.
}\)

First of all , you need to prove that the triangles are similar.

Answer 8

@ScarlettBlack , may be you did a mistake in calculation :

\( = \sqrt{(21-8)^2 + (32-17)^2 } \)

Which I get : 19.849 units or 20 units.

Answer 9

Ok, yes I made a mistake in the second calculation.

Answer 10

Yes. Now, for the second one, can you prove those 2 triangles similar?

Answer 11

For the second one. I thought the ratio was 4:5

Answer 12

Yes, good, the ratio of AR : AE = 4 : 5

Answer 13

But before you use the theorem I provided, you need to prove that the 2 triangles are similar. Do you have any ideas for this?

Answer 14

Well they share a common angle

Answer 15

http://www.ask-math.com/basic-proportionality-theorem.html

You will have to use Basic Proportionality Theorem to prove that the ratio of the corresponding sides is equal to the ratio of AR and AE . Then, you can easily state that since the ratios of the corresponding sides is equal , thus, the triangles will be similar.

Have you learnt Basic Proportionality Theorem?

Answer 16

Yes.

Answer 17

So, use this theorem.

Answer 18

I actually have to go now. I'm visiting a friend in the hospital. Thanks for the help. I will definitely do the rest.

Answer 19

Oh. Get well soon to your friend. Have a great day ahead! Let me know if you have any doubts.